Imagine for a minute that the moon is held in its orbit aboutthe Earth by electr

Question

Imagine for a minute that the moon is held in its orbit aboutthe Earth by electrical forces rather than bygravitation. What electrical charges -Q on the Earth and +Qon the moon are necessary to hold the moon in a circular orbitwith a period of 27.3 days? The Earth-moon distance is384,000 km and the mass of the moon is 7.35 x 1022 kg. Imagine for a minute that the moon is held in its orbit aboutthe Earth by electrical forces rather than bygravitation. What electrical charges -Q on the Earth and +Qon the moon are necessary to hold the moon in a circular orbitwith a period of 27.3 days? The Earth-moon distance is384,000 km and the mass of the moon is 7.35 x 1022 kg.

Explanation / Answer

the mass of the Earth is very large compared to this of themoon, therefore we can estimate the motion ofthe moon is around the center of the earth. with radiusof 384000 km
from the Coulomb's Law electric force gives the centripetal acceleration k*Q2 /r2=m*v2/r =>Q2=m*v2*r/k (1) the period: T=2r/v =>v=2r/T from (1) =>Q2=m*(2r)2*r/(k*T2) ; T=23.7days => Q=5.72*1013 C

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